Global weak solutions for an Newtonian Fluid interacting with a Koiter\n Type Shell under natural boundary conditions

2018/07/19 by Hannes Eberlein, Eberlein, Hannes, Michael Růžička +1
Chemical Engineering · Computer Science · Mathematics · #74F10 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.1807.07348

openalex publication_date 2018/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an viscous, incompressible Newtonian fluid flowing through a thin\nelastic structure. The motion of the structure is described by the equations of\na linearised Koiter shell, whose motion is restricted to transverse\ndisplacements. The fluid and the structure are coupled by the continuity of\nvelocities and an equilibrium of surface forces on the interface between fluid\nand structure. On a fixed in- and outflow region we prescribe natural boundary\nconditions. We show that weak solutions exist as long as the shell does not\nself-intersect.\n

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